Real-scale 3D models of the scoliotic spine from biplanar radiography without calibration objects Daniel C. Moura a , Jorge G. Barbosa b,c a Instituto de Telecomunica¸ c˜ oes, Departamento de Engenharia Electrot´ ecnica e de Computadores, Faculdade de Engenharia, Universidade do Porto, Porto, Portugal daniel.moura@fe.up.pt b Departamento de Engenharia Inform´ atica, Faculdade de Engenharia, Universidade do Porto, Porto, Portugal c Laborat´ orio de Intelegˆ encia Artificial e Ciˆ encia dos Computadores, Porto, Portugal Abstract This paper presents a new method for modelling the spines of subjects and making accurate 3D measurements using standard radiologic systems without requiring calibration objects. The method makes use of the focal distance and statistical models for estimating the geometrical parameters of the system. A dataset of 32 subjects was used to assess this method. The results show small errors for the main clinical indices, such as a RMS error of 0.49 ◦ for the Cobb angle, 0.50 ◦ for kyphosis, 0.38 ◦ for lordosis, and 2.62 mm for the spinal length. This method is the first to achieve this level of accuracy without requiring the use of calibration objects when acquiring radiographs. We conclude that the proposed method allows for the evaluation of scoliosis with a much simpler setup than currently available methods. Keywords: Calibration, Stereoscopy, Radiography, Vertebra localisation, Statistical modelling, 3D Reconstruction 1. Introduction Developing methods for creating three-dimensional (3D) spinal reconstructions from two planar x-ray images has been an active research topic due to the clinical evaluation improvements allowed by a 3D model of the spine in a standing position. Three-dimensional reconstructions are mainly required to evaluate spinal deformities, such as id- iopathic scoliosis, which are 3D in nature and consequently cannot be conveniently assessed by planar radiography. Examples of clinical indices that can only be quantified with a 3D model of the spine include the plane of maximum curvature, vertebrae axial rotation [1], and the three-dimensional spinal length [2]. Additionally, 3D spinal reconstruc- tions are important for making personalised biomechanical models of patients’ spines that may be used for guiding therapy (e.g. [3, 4]). In this paper, 3D reconstruction of the spine means that we can position the vertebrae in 3D so that we have an accurate representation of the spine that allows us to obtain accurate clinical indices, as illustrated in Figure 1. Reconstruction techniques can be divided into methods that require full manual annotation of the x-rays and methods that reduce the user interaction. Manual methods are the most well-known techniques and require an expert to manually identify a set of point-matches from two radiographs (i.e., frontal and lateral planes). In [5], a set of 6 stereo-corresponding points per vertebra were used (i.e., centres of the superior and inferior endplates and the superior and inferior extremities of the pedicles); in [6], this set was augmented with non-stereo corresponding points to better capture vertebrae shape. Finally, in [7], the number of landmarks was decreased to 4 per vertebrae per radiograph due to the use of statistical models. More recently, other techniques strongly based on statistical models and/or image analysis have further reduced user interaction, typically requiring fewer than ten points per view [8, 9, 10, 11, 12, 13, 14]. Attempts have also been made to develop quasi-unsupervised methods, but only for the lower part of the spine [15, 16]. Independent of their specific approach, all of these methods need to know the geometry of the radiological system, including the patient position and orientation, to compute 3D data from the 2D data of the planar radiographs. These Preprint submitted to Computerized Medical Imaging and Graphics Thursday 29 th May, 2014